Swedroe: Building Optimal Value Portfolios

September 23, 2015

In 1981, Sanjoy Basu’s paper, “The Relationship Between Earnings’ Yield, Market Value and Return for NYSE Common Stocks,” found that the positive relationship between the earnings yield (E/P) and average return is left unexplained by market beta.

Then, in 1985, Barr Rosenberg, Kenneth Reid and Ronald Lanstein uncovered the positive relationship between average stock returns and book-to-price (B/P) ratio in their paper, “Persuasive Evidence of Market Inefficiency.”

Together, these two studies provided evidence that a value premium existed. And even though there are several different metrics that can be used to determine value—such as E/P, B/P, dividend-to-price (D/P), cash flow-to-price (CF/P), sales-to price (S/P) and EBITDA-to-price (EBITDA/P) ratios—since the 1992 publication of Eugene Fama and Kenneth French’s seminal paper, “The Cross-Section of Expected Stock Returns,” the most commonly used metric has been book-to-price.

‘Optimizing Value’

In their May 2015 paper, “Optimizing Value,” Ran Leshem, Lisa Goldberg and Alan Cummings of the Aperio Group investigated how the choice of accounting metric, and the implementation of it, affect the performance of a value strategy. Using the data from Kenneth French’s website, as well as from MSCI Barra, they examined outcomes from two value metrics—B/P and E/P (the earnings yield, or earnings-to-price ratio—for the period 1951 through 2013.

The authors found that while strategies based on either B/P or E/P each delivered positive premiums over the full period, the E/P metric outperformed B/P by, on average, 1.17 percentage points per year (15.99 versus 14.82). What’s more, it did so with slightly less volatility.

However, the results weren’t uniform over the full period. They noted that over the period covered in the original Fama and French paper (July 1963 through December 1990), B/P outperformed E/P by 1.06 percentage points per year (15.35 versus 14.29), and that it did so with virtually the same volatility. In the subsequent period (January 1991 through December 2013), E/P outperformed B/P.

Diversification Blend Outperforms

The authors also found that, due to a diversification benefit, a 50/50 blend of B/P and E/P outperformed both single-metric strategies during most 10-year periods between 1973 and 2013. The blended strategy had the highest annualized return: 14.21 percent per year over the period January 1973 through December 2013, followed by E/P with 13.48 percent per year and B/P with 12.79 percent per year.

Turning to risk, E/P had the lowest standard deviation, coming in at 16.41 percent versus 17.36 percent for the blended strategy, and 18.79 percent for B/P. E/P also had the lowest tracking error against the S&P 500 Index: 7.04 percent versus 8.13 percent for the blended strategy, and 9.27 percent for B/P. The blended strategy had the highest Sharpe ratio, at 0.53, versus 0.52 for E/P and 0.44 for B/P. Turnover rates were similar and, as a result, so were estimated trading costs (they were within 1 basis point).

Tracking Error Risk

Leshem, Goldberg and Cummings also found that investors concerned with the tracking error risk of value-tilted portfolios should consider using an approach that constrains the divergence in sector weightings to the index while still maintaining the value tilt.

Using the S&P 500 as their benchmark, the authors found that restricting the sector weights to within 1 percent of the benchmark weightings could cut tracking error by more than 50 percent, while also reducing turnover and transaction costs (by about 10 bps). Over the period studied, the sector-constrained approach outperformed as well.

Returns To 4 Value Metrics

Last year, I took a look at the returns to different value metrics. The table below shows the premium and the t-stat for each of four commonly used value metrics. Note that premiums are always determined from long/short portfolios.

Annual Average Returns 1952-2013

Value Metric Average Annual Return (%) T-Statistic
Dividend-to-Price (D/P) 2.17 0.87
Book-to-Price (B/P) 4.43 2.54
Cash Flow-to-Price (CF/P) 5.11 3.19
Earnings-to-Price (E/P) 7.33 5.00


Clearly, sorting by almost any metric scaled by price will generate a positive expected return. Each of the four value portfolios generated higher annualized returns than the overall market.

However, as you can see, the D/P ratio, while it provides exposure to the value premium, has produced the lowest returns. The D/P premium is also the only one that wasn’t statistically significant. In other words, while a high-dividend strategy is a value strategy, it’s a weak one.

B/P More Commonly Used

In addition to its strong performance during the period covered by the original Fama and French research, the B/P metric commonly has been used to determine value because the book value of a company, being a cumulative measure, is more stable than E/P.

This is important because the more volatile a metric used, the higher the turnover of the strategy might be, and the less tax efficient it will become. (Note that the authors found very similar turnover rates whether they used B/P or E/P.) And while strategies have no costs, implementing a strategy does.

This is especially critical when constructing portfolios of small-cap value stocks, as well as for taxable accounts. Another argument in favor of using the B/P metric is that E/P can more easily be manipulated than either the book value or cash flow metrics.

Various Approaches Being Used

Some fund companies have developed strategies that use multiple metrics with various weighting schemes, believing this approach provides a diversification benefit. While the correlation of returns to each of the four metrics is highly positive, they aren’t perfectly so.

Another reason for using the E/P and CF/P metrics in the portfolio construction rules of a value strategy is related to the relatively new profitability factor. The research has found that the E/P and CF/P factors, as well as a multifactor approach, provide greater exposure to the profitability factor than B/P.

The various fund families and indexes that use the academic literature in designing construction rules for their value funds or indexes include:

  • Dimensional Fund Advisors (DFA), which previously used the single metric of book value, recently added a gross profitability measure.
  • Bridgeway and Vericimetry both use a combination of four metrics relative to price: sales, earnings, cash flow and book value.
  • AQR uses five metrics: book-to-price, earnings-to-price, forecasted earnings-to-price, cash flow from operations-to-enterprise value (defined as market capitalization plus debt plus preferred equity minus cash) and sales-to-enterprise value.
  • Vanguard’s index funds track Center for Research in Security Prices (CRSP) indexes, which use a combination of book value, earnings and dividends.
  • RAFI employs a combination of sales, cash flow, book value and dividends.
  • Russell uses the book-to-price ratio to represent value and I/B/E/S forecast medium-term growth and historical sales per share growth to represent growth.
  • MSCI uses a combination of sales, earnings, cash flow and book value.


While I don’t think there is a large difference between the various value measures (with the exception of D/P), I do believe there’s value in using multiple metrics.

The logic is this: There are problems associated with all the commonly used metrics, and they show up to varying degrees in different industries or sectors. By using multiple metrics, investors are, in a sense, diversifying their exposure to any of these issues.

In addition, we know that the relative performance of each metric is period-dependent. Thus, using a multiple-metric approach should provide a diversification benefit, while also somewhat reducing tracking error.

Finally, in the interest of full disclosure, my firm, Buckingham, recommends AQR, Bridgeway and DFA funds in constructing client portfolios.

Larry Swedroe is the director of research for The BAM Alliance, a community of more than 140 independent registered investment advisors throughout the country.

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